How to dynamically show/hide panel elements using python?
The solution was so trivial I didn't expect it to be. It's a matter of simply adding a conditional to the panel draw function:

class SomePanel(bpy.types.Panel):
    bl_idname      = "the_panel"
    bl_label       = "Panel with some controls"
    bl_space_type  = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context     = "object"

    def draw(self, context):
        layout = self.layout
        scene = context.scene

        layout.prop(scene, "is_enabled")

        if scene.is_enabled:
            layout.operator("object.select_random") # As an example.